# The Euclidean algorithm in quintic and septic cyclic fields

@article{Lezowski2017TheEA,
title={The Euclidean algorithm in quintic and septic cyclic fields},
author={Pierre Lezowski and Kevin J. McGown},
journal={Math. Comput.},
year={2017},
volume={86},
pages={2535-2549}
}
• Published 2017
• Mathematics, Computer Science
• Math. Comput.
Conditionally on the Generalized Riemann Hypothesis (GRH), we prove the following results: (1) a cyclic number field of degree $5$ is norm-Euclidean if and only if $\Delta=11^4,31^4,41^4$; (2) a cyclic number field of degree $7$ is norm-Euclidean if and only if $\Delta=29^6,43^6$; (3) there are no norm-Euclidean cyclic number fields of degrees $19$, $31$, $37$, $43$, $47$, $59$, $67$, $71$, $73$, $79$, $97$. Our proofs contain a large computational component, including the calculation of the… Expand
4 Citations